Abstract

We analyze the Cp–T data for the glassy state of eight materials of varied molecular interactions and structures to investigate how the use of the Cpd ln T integral in the time-dependent (nonreversible) thermodynamic path between a liquid and glass affects our estimates of the entropy. Since the change in entropy on such a path cannot be determined, we estimate the upper and lower values of the change, Δσ, from the Cpd ln T integral. For the same rates of cooling and heating and without annealing, Δσ on the cooling path is negligibly different from that on the heating path. The difference is ∼1/60th–1/25th of the lowest known value of the residual entropy and even less than the configurational entropy of the supercooled liquid at its kinetic freezing temperature. Thus use of the Cpd ln T integral in the nonreversible path does not introduce significant errors in estimating the residual entropy. Dynamic Cp data cannot be used to infer that configurational entropy decreases on glass formation. Time dependence of the Cp–T path has little consequence for reality of the residual entropy.

We thank Dr. Ulrich Fotheringham of Schott AG, Mainz, Germany, for providing their published data for the silica-based glasses, and Martin Goldstein for comments on this study. This research was supported by a Discovery Research Grant from NSERC of Canada.